1. ( \(\sigma\) assumed known). A dairy refuses to accept raw milk having more than 5000 bacteria per milliliter \((\mathrm{mL})\). The bacteria count varies from shipment to shipment. Assume that the count of bacteria per milliliter is normally distributed with a population standard deviation of 16 . The dairy wants to test that the mean bacteria count is less than 5000 per \(\mathrm{mL}\) for the next shipment. A simple random sample of 64 1-mL samples from the next shipment resulted in a mean bacteria count of 4995 .

1. State the null and alternative hypothesis for this problem.
2. Calculate the observed test statistic value.
3. Report the \(p\) -value for this test.
4. Are the results statistically significant at the \(1 \%\) level of significance? Explain.

2. In the past, the average length of stay of tourists in a city's hotels has been 3.1 nights. A new marketing campaign to promote the attractiveness of the city has been in place for the last two months. An analyst is to test whether the new campaign has increased tourism. The analyst obtained a random sample of the number of nights spent by tourists in the city's hotels after the campaign started.

\(\begin{array}{llllllllllll}

8 & 4 & 6 & 2 & 3 & 5 & 1 & 2 & 3 & 4 & 7 & 3

\end{array}\)

We wish to assess whether there is enough evidence to conclude that the mean number of nights spent at a hotel is higher than 3.1.

3. Authorities in Detroit, MI, suspect that the introduction of fluoride to the drinking water will significantly reduce the average number of cavities among children. Last year, the average number of cavities was \(\mu=2.6\). This year, fluoride was introduced, and, for a sample of 36 children, an average of 1.5 cavities was found with a standard deviation of 0.75.

Using \(\alpha=0.05\), test the hypothesis of the authorities in Detroit.

Problem 4: The value reported as lost for a random sample of \(n=20\) pickpocket offenses occurring in a city is given here.

Use the data to construct a \(95 \%\) confidence interval for the mean value lost in all pickpocket offenses for this city.

5. An investigator believed that people who smoke tend to smoke more during periods of stress. He compared the number of cigarettes ordinarily smoked by a group of 18 randomly selected students with the number they smoked during the 24 hours prior to a final examination. Test the appropriate hypotheses using a significance level of \(10 \%\). Show all steps

6. A toothpaste manufacturer claims that children brushing their teeth daily with his company's new toothpaste product will have fewer cavities than children using a competitor's brand. In a carefully supervised study in which children were randomly assigned to one of the two brands of toothpaste for a 2-year period, the number of cavities for children using the new brand was compared with the number of cavities for children using the competitor's brand. The results are as follows:

New Brand: 2,1,1,2,3,1,2,3,4,1,2

Competitor Brand: 3,1,1,4,0,7,1,1,4,6,1

Test the manufacturer's claim using a significance level of 0.01

7. A study was performed to compare two cholesterol-reducing drugs. Data on the number of units of cholesterol reduction were recorded for 12 subjects randomly assigned to Drug 1 and the remaining 14 subjects who received Drug 2 . These data are summarized in the following table:

Construct a \(95 \%\) confidence interval for the difference between the population mean cholesterol reduction for Drug 1 and the population mean cholesterol reduction for Drug 2.

8. Two creams are available by prescription for treating moderate skin burns. A study to compare the effectiveness of the two creams is conducted using 15 randomly selected patients with moderate burns on their arms. Two spots of the same size and degree of burn are marked on each patient's arm. One of the two creams is selected at random and applied to the first spot, while the remaining spot is treated with the other cream. The number of days until the burn has healed is recorded for each spot. These data are provided along with the difference in healing time (in days).

Construct the \(95 \%\) confidence interval for estimating the mean difference in healing time, \(\mu_{0}\).

Price: $21.77

Solution: The downloadable solution consists of 9 pages, 1277 words and 5 charts.
Deliverable: Word Document